Optimal Control Problems in Collaborative Multi-agent Robotic Systems

The paper considers human-robot collaboration from the control point of view as the joint activity of robots and people in a single multi-agent system to achieve the desired objective with the optimal value of a quality criterion. The paper proposes a mathematical statement of the control problems for such complex plant. In the proposed formulation, the role of a person is described in the form of an additional control vector, with the help of which the influence of phase constraints is reduced in terms of functional minimization. So, the problem statements of the optimal control and the control general synthesis problems for collaborative systems include additional control vector in phase constraints. The problems are formulated for a single collaborative cell and for multi-agent collaborative system. The problem statements for multi-agent systems include also dynamic phase constraints to avoid collisions between robots. The problems of collaborative control in the proposed formulations can be solved by modern numerical methods of machine learning control. An example of optimal control problem for two mobile robots with two controlled phase constraints as operational zone for human-operators is presented. The problem is solved using machine synthesized optimal control method.